Hellwig was born in Garz, Pomerania, son of Friedrich Ludwig Wilhelm and Dorothea nee Kolbe. After studies of
mathematics and
natural history at the university of
Frankfurt, he became, in 1766, adviser to prince
Wilhelm Adolf von Braunschweig at the time of his grand tour in the south of Russia. The prince died during this journey at
Oczakow and Hellwig returned to Braunschweig (Brunswick) in 1770. In 1771, he was appointed teacher of mathematics and natural sciences in two colleges of Brunswick. In 1773 he received a doctorate from the University of Helmstedt. In 1790 he was appointed to teach mathematics and natural sciences at the Collegium Carolinum in Braunschweig, becoming full professor in 1802. He taught mathematics when the College Carolinum was converted to the military academy of
Braunschweig. Teaching military sciences inspired his work on wargames. A number of his students became significant mathematicians:
Conrad Diedrich Stahl, professor in Jena, then in Landshut and later in Munich, Karl Bartels, state councilor and professor in Dorpat,
Brandan Mollweide in Leipzig, the astronomer
A.H. Christian Gelpke in Braunschweig,
Friedrich Wilhelm Spehr in Brunswick,
Karl Graeffe in Zurich and
Karl Friedrich Gauss. He was the tutor and the father-in-law of the German entomologist
Johann Karl Wilhelm Illiger (1775–1813), who became director of the zoological garden of
Berlin, of the mineralogist
Gottlieb Peter Sillem (who also became a son-in-law and succeeded him at the school of Braunschweig) and the count
Johann Centurius Hoffmannsegg (1766–1849). At his death he had served the state of Brunswick for 60 years and the ducal family for 65 years. He founded the Brunswick general widows’ fund, now a general life insurance institution, and was responsible for the actuarial calculations ensuring its viability. He worked in the taxonomy of the insects in collaboration with
Illiger and
Hoffmannsegg, and his insect collection, together with theirs, was the origin of the insect collection of the
University of Berlin. == Hellwig's wargame ==